Question 1
A linear association with a correlation coefficient of 0.23 is best described as
That’s it. Step through the hints below to see why. In 2023, 84.0% of Queensland students chose (A).
Not quite. Weak is right, and the direction is where it slips. The sign of $r$ gives the direction, and $0.23$ has no minus sign, so the association is positive. A negative association would need a value like $-0.23$. In 2023, 7.3% of Queensland students chose (B).
Not quite. Positive is right, but $0.23$ is much closer to 0 than to 1. A strong association needs $r$ near 1, where the points hug a straight line. At $0.23$ they barely follow one. In 2023, 4.9% of Queensland students chose (C).
Not quite. Both words are off. $0.23$ has no minus sign, so the association is positive, and it sits close to 0, so the association is weak. In 2023, 3.3% of Queensland students chose (D).
Drag $r$ from $-1$ to $1$. The sign tilts the cloud, the size tightens it. The strip underneath shows where your value sits under the usual convention.
Every option is two words, a strength and a direction. Get the direction first, because it is the quicker read.
The sign of $r$ is the direction. A plus (or no sign at all) means positive: as one variable increases, the other tends to increase. A minus means negative.
$0.23$ has no minus sign, so it is positive. That rules out (B) and (D).
The size of $r$ is the strength. The closer $r$ is to $1$ or $-1$, the tighter the points sit around a line. The usual convention:
| $0.75\le |r|\le 1$ | strong |
| $0.5\le |r|<0.75$ | moderate |
| $0.25\le |r|<0.5$ | weak |
| $|r|<0.25$ | no association |
$0.23$ is nowhere near the strong row, so (C) is out as well.
Look closely and $0.23$ sits just under the weak row, at the top edge of “no association”. That isn’t one of the options.
This is why the question says best described. The syllabus names strong, moderate and weak, but the cut-offs are a teaching convention, not part of the syllabus. Of the four options, weak positive is the only one that gets both the direction and the size of $0.23$ about right.
Press Go to $r=0.23$ on the left. The cloud leans uphill, only just.
Direction: $r=0.23>0$, so the association is positive.
Strength: $|r|=0.23$ is close to 0 and far from 1, so the association is weak. Of the options given, weak is the best fit.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording is from the 2023 QCAA General Mathematics external assessment, © State of Queensland (QCAA) 2023, licensed under CC BY 4.0, and has been adapted. Tangent Tuition is not affiliated with the QCAA.
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